> Also, I wonder why you want to decompose on both X and Y ("pencils"),
> and not only X ("books"),
> which may give you a smaller/simpler domain decomposition
> and communication footprint.
> Whether you can or cannot do this way depends on your
> computation, which I don't know about.

I'm not sure I'm following the entire thread, but higher-dimensional
decompositions, though more complicated, can improve the
communciation:computation ratio. For example, say you have a
100x100x100 grid to distribute over 100 processes. Even if you have
only one ghost cell at each surface, a 1d decomposition would place a
1x100x100 "book" on each process with 2x100x100 ghost cells: a 2:1
ratio of ghost:real cells! That's a lot. In contrast, if you had
10x10x100 pencils, there would be (4*10+4)x100 ghosts. The ratio drops
to 0.44. This is an extreme case, but it illustrates the point.

Indeed, maybe you could even drop to a 25x20x20 "box". Then the
ghost:real ratio might be around 0.29 or so.